First off... Don't drop the laptop... they don't bounce well.
From the symptoms you have described I would guess that something has been partially disconnected at best or broken and failing and must be replaced at worst.
BACKUP UP YOUR DATA NOW -- YOU RUN THE RISK OF DATA LOSS IF YOUR COMPUTER FAILS AND TAKES OUT THE DRIVE.
WARNING -- TECHNICAL EXPERTISE IS REQUIRED FOR SERVICE AND REPAIR OF LAPTOPS!!!!
The fact that the system powers up and runs is a good sign. That being said it is most likely that the keyboard has been damaged in the fall. Perhaps you can get away with removing the keyboard and re-seating all the cable connections.
Unfortunately there is also the possibility that the damage has occurred on the motherboard itself. This will involve replacement of expensive components, if replacement is possible. One other potential problem might arise from the damage having caused an intermittent short in the system, if this is the case continued use will eventually short out the component and cause substantially more damage.
I would suggest that finding a technician or repair service to look at your system might be advisable. You will also want to price out the cost of repairs vs the replacement of the computer system, since laptop components are outrageously expensive and sometimes very difficult to obtain.
Sadly, this may not be what you want to hear, but laptops are pretty fragile items... that they last as long as they do is somewhat surprising to me, and I've been repairing them for just about 10 years.

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